Question

Compare the quantity in Column A and the quantity in Column B. Then determine whether:

(A) The quantity in Column A is greater,

(B) The quantity in Column B is greater,

(C) The two quantities are equal, or

(D) The relationship cannot be determined from the information given.

19.

Column A: The percent increase from 75 to 100.

Column B: The percent decrease from 100 to 75.

Short answer

The correct option is (A) the quantity in column A is greater, the other options are wrong because the value of the percent increase from 75 to 100 is 33.

This is greater than the value of the percent decrease from 100 to 75 is -25.

Step-by-step solution

– Compute the value of the quantity in column A.

Find the percent increase from 75 to 100.

The formula for the percent increase$=\frac{\text{new value}-\text{old value}}{\text{old value}}\times 100\%$.

Here the new value is 100, old value is 75.

Then,

$\begin{array}{c}\text{percent}=\frac{\text{newvalue}-\text{oldvalue}}{\text{oldvalue}}\times 100\%\\ \text{percent}=\frac{100-75}{\text{75}}\times 100\%\\ =\frac{25}{75}\times 100\%\\ =33.333\%\end{array}$

So, the percent increase from 75 to 100 is 33.33%.

– Compute the value of the quantity in column B.

Find the percent decrease from 100 to 75.

The formula for the percent increase$=\frac{\text{new value}-\text{old value}}{\text{old value}}\times 100\%$.

Here the new value is 75, old value is 100.

Then,

$\begin{array}{c}\text{percent}=\frac{\text{newvalue}-\text{oldvalue}}{\text{oldvalue}}\times 100\%\\ \text{percent}=\frac{75-100}{\text{100}}\times 100\%\\ =\frac{-25}{\text{100}}\times 100\%\\ =-25\%\end{array}$

So, the percent decrease from 100 to 75 is -25%.

– Check whether the option A is correct or incorrect. 

The value of the quantity in column A is 33.33% and the quantity in column B is -25%.

This means the quantity in column A is greater.

So, the option A is correct.

– Check whether the option B is correct or incorrect. 

The value of the quantity in column A is 33.33% and the quantity in column B is -25%.

This means the quantity in column B is less than the quantity in column A.

So, the option B is incorrect.

– Check whether the option C is correct or incorrect. 

The value of the quantity in column A is 33.33% and the quantity in column B is -25%.

Here the values of the two quantities in column A and column B are different.

So, the option C is incorrect.

– Check whether the option D is correct or incorrect. 

The value of the quantity in column A is 33.33% and the quantity in column B is -25%.

Here the values of the two quantities in column A and column B are two different values, one can determine a relationship between the quantities.

So, the option D is incorrect.

Hence, the correct option is (A) the quantity in column A is greater, the other options are wrong because the value of the percent increase from 75 to 100 is 33.

This is greater than the value of the percent decrease from 100 to 75 is -25.